Scavenger's Den - Cavern with Metal Cages

On the low ramp on the right is another brazier where you can relight your torch.

Above are two dangling cages tethered together by some kind of pulley system. Use the torch to burn the two cloth-wrapped poles. This releases the ropes anchoring the lower cage so it drops into the water. In this position, it begins to collect the debris floating downstream. Simultaneously, the other cage is raised up.

Go up the ramp on the right and around to the middle of the wooden ledge.

Jump from there into the raised cage.

Lara's weight lowers that cage, raising the one containing the debris, which is then dumped into a third cage at the end of the wooden ledge.

Hop down to the ground. Then go up the ramp again and continue around to the end.

Stand close to the cage and press Interact to light the debris on fire.

Then press the Melee button (F on the PC, Triangle on the PS3 or Y on the Xbox 360) to shove the crate off the edge.

It slides down into the water, carrying flaming debris into the barricade and causing an explosion that clears the way.